ArticleOriginal scientific text
Title
Nonnegative solutions of a class of second order nonlinear differential equations
Authors 1
Affiliations
- Department of Mathematical Analysis, Faculty of Science, Palacký University, TŘ. Svobody 26, 771 46 Olomouc, Czechoslovakia
Abstract
A differential equation of the form
(q(t)k(u)u')' = λf(t)h(u)u'
depending on the positive parameter λ is considered and nonnegative solutions u such that u(0) = 0, u(t) > 0 for t > 0 are studied. Some theorems about the existence, uniqueness and boundedness of solutions are given.
Keywords
nonlinear ordinary differential equation, nonnegative solution, existence and uniqueness of solutions, bounded solution, dependence of solutions on a parameter, boundary value problem
Bibliography
- F. V. Atkinson and L. A. Peletier, Similarity profiles of flows through porous media, Arch. Rational Mech. Anal. 42 (1971), 369-379.
- F. V. Atkinson and L. A. Peletier, Similarity solutions of the nonlinear diffusion equation, ibid. 54 (1974), 373- 392.
- J. Bear, D. Zaslavsky and S. Irmay, Physical Principles of Water Percolation and Seepage, UNESCO, 1968.
- J. Goncerzewicz, H. Marcinkowska, W. Okrasiński and K. Tabisz, On the percolation of water from a cylindrical reservoir into the surrounding soil, Zastos. Mat. 16 (1978), 249-261.
- W. Okrasiński, Integral equations methods in the theory of the water percolation, in: Mathematical Methods in Fluid Mechanics, Proc. Conf. Oberwolfach 1981, Band 24, P. Lang, Frankfurt am Main 1982, 167-176.
- W. Okrasiński, On a nonlinear ordinary differential equation, Ann. Polon. Math. 49 (1989), 237-245.
Pages:
71-82
Main language of publication
English
Received
1991-02-15
Accepted
1991-06-30
Published
1992
Exact and natural sciences